Thousands of people joined May Day demonstrations in the capital cities on Sunday to vent their anger about the Coalition government’s possible cut to the minimum wage in next week’s budget.

The protesters were buoyed by a poll, published by News Corp Australia on Sunday, showing the government would lose office if an election were held today. However, with an election not due until 2016, trade unionists fear the minimum wage will be cut, as recommended by the National Commission of Audit on Thursday.

The president of the Queensland Council of Unions, John Battams, said if the minimum wage was cut from $16 to $12 an hour, it “would result in a huge pool of working poor”, as in the United States.

“About one-and-a-half million Australians depend on the minimum wage to actually make ends meet,” Battams said.

The Labor party leader in Queensland, Annastacia Palaszczuk, said the 25,000-strong demonstrations in the state sent a strong message to the government. “We can sense the winds of change. People are not happy with this government,” she said.

In Brisbane, many of the protesters’ placards criticised the premier, Campbell Newman, who has made deep cuts to the public service.

Most of the approximately 5,000 marchers in Melbourne were expressing their fears about the future of their pay and work because of the federal government's proposed changes, the city's May Day committee organiser, Len Cooper, said.

“People are pretty edgy about the future of pay, conditions, social conditions, work conditions. Everything is up in the air in their minds,” Cooper said.

Protesters also spoke out about the treatment of refugees, changes to Victorian laws concerning protest rights and the dangers of free-trade deals.

In Sydney, the approximately 7,000-strong crowd protested about the New South Wales government’s plan to privatise the state's $30 billion electricity infrastructure.

Paul Lester of the Electrical Trades Union had a message for the premier. “Mike Baird is his name, privatisation is his game. We all know what you're about. Come next May we will throw you out.”

As NSW treasurer, Baird supported privatising the electricity infrastructure and has flagged, since becoming premier, that he would be seeking a mandate on the issue at the next election.

May Day commemorates the events of 4 May, 1886, when trade unionists in Chicago demanding an eight-hour day came under fire. Four demonstrators were killed.